Share encoded radix traversal in directory production

[ToikY]

Change and mathematical scope

Share one encoded radix traversal across the directory producer's fixed matrix coordinates. The package-local high_power_shared replaces only the binding used by the unchanged retained directory.produce; no shared/frozen runtime or selected record is edited. Both versions perform the same ordered d²(w−1) Count multiplications by q, so returned count, complete output bytes/order, physical duplicate multiplicity, record/index traffic, protected state and successful cleanup agree.

For M=d², exact source residue-Word saving is (M−1) rho(q,w,L), where rho is the complete validated radix traversal's reads/writes/unit moves. At dimension64/cap1, residue actions fall (2793472,483328,2916352) → (651787,94303,639532): 2,141,685 reads, 389,025 writes and 2,276,820 moves saved. Record Tape (310027,91612,274870) and index Word (15,0,12) remain unchanged. The credited additional numerical peak remains4096. This is a source-action saving, not a measured wall-clock or physical bit-machine claim.

The successful valid-input interval begins with an already-live Context. Context construction/close, input/vocabulary compilation, returned-object disposal and all other caller phases remain explicit separate charges. The actual Machine.residual_begin call is retained as authenticated evidence. The dimension64 fixture uses Q=6507 with projected valid vocabulary, not full selected source/LowCodes admission; nontrivial full high cubes are bounded small dimensions. No multi-lift dimension64 run, whole Pi, physical reserve, selected m73 stock coefficient, supplier or new κ is claimed. Inherited malformed-input paths are not promised general exception rollback.

Evidence

Only research/directory-producer-invoice/ is added:18 files, one canonical-parent commit 84bd28ef6da3a3473d14a48088f30ba82d414450.

python3.12 -B scripts/research_package.py --package research/directory-producer-invoice

Seven complete original/candidate pairs cover q2/3/5, dimensions1/2/3/64, long carries, empty/repeated prefixes and varying depths/widths. All eight source exports authenticate before execution. Primary metering includes every borrowed/created Tape, Count/Counter, residue/index Word, output and rewind; radix exhaustion and ordered multipliers are traced. A separate no-import checker derives every action lane and directly serializes whole expected outputs. PROOF.md gives the arbitrary-valid-input composition and exact invoice.24 semantic/integrity rejections plus3 positives pass under normal and optimized Python, including cap1 variants that preserve output while wrongly skipping validation.

Local CPython3.12.14 registered replay, whitespace and exact18-file publication-byte/source-history preflight pass. Official committed export/check pass. All three commands pass normal and optimized in a fully read-only19-file Git-free export with empty PATH/PYTHONPATH; all bytes, modes and inodes remain unchanged. Archive SHA256 d69ec07aa953f46f8e5169df419a66e9dd8193104ca5ed7d1bd49924557896ab. Hosted CI39233311002 passes at this exact head:265 onboarding tests (11skips), only this package selected, all3 registered commands on CPython3.12.15, and unchanged committed inputs. The runner checked synthetic merge f5a7edd of this head into canonical20ec.

Task, overlap and predecessor credit

Handoff-first changed selected-stock-envelope scope; exact card, baseline failure and narrower question in TASK.json. Canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority6, catalogue/selected hashes and adjacent #4011 head refreshed unchanged. Entry724 open PR bodies completely paginated; latest100-body delta through4023, repository helper, retained packages and bounded live1166/source/active-board checks. Broader Discussion/closed/code coverage partial. Claim, narrowing update.

ywz65/#2590 already proves cubic repeated setup and complete Theta_q(D), and explicitly asks for this shared traversal. The old asymptotic/serialized-size/multiplicity claims are not new. ywz65's directory-storage allowance and Ross Richardson's exact max(d²,6) numerical peak are credited prior results; neither changes here. Fixed-dimension cubic width order remains. Jose Manuel/jmbarrancoml supplies the runtime/physical caller; David Arias/#2753, Nick Petalas and retained stream/controller/record lineage retain credit and the complete original notice. ywz65/#2566 supplies primitive analysis. Chris R/Clear1nsight #3983/#4011 supplies adjacent preparation/admission work. New work by ToikY with substantial OpenAI Codex assistance and separate AI math/test contexts, Apache-2.0; no independent human or formal-kernel acceptance.

Open next questions

Review/admit this exact candidate into a complete caller with fixed control/allocator tariffs. Join Context, geometry, child_extents/read_prefix, coefficients and other Pi phases, then all simultaneous dirty/parent/child/Count/template/backing lifetimes at original widths before a physical reserve or recursive claim. Unknown costs remain unknown. Maintainer edits disabled; no merge, closure or frontier change.

Discussion handoff. Claim released; no continuing reservation.